Problems of Computational Mathematics (On the Best Algorithms in Numerical Mathematics)

Abstract:

The renowned physisist Albert A. Michelson together with Edward W. Morley during the experiment performed between April and July 1887 at what is now Case Western Reserve University in Cleveland, Ohio, measured the speed of light in vacuum, commonly denoted c, which is a universal physical constant important in many areas of physics. Its exact value is 299792458 metres per second. Later he established the independence of the speed of light from the speed of the Earth in orbital motion. Then the hypothesis on the constancy of the light speed at any point of the Universe appeared. What is following. Imagine the Computer in which the main element is of size h cm and this Computer permorms the arithmetic operation when a signal passes through it at the speed of light. The speed of such a machine is c/h operation per second. We omit the time needed for signal passage through other elements of a machine. The less is the size h of an element the greater is the operational speed. Imagine that engineers succeded in construction of the machine with the elements as small as 10-8 cm (the size of an atom).

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